(1) Field of the Invention
The present invention relates generally to methods for measuring material characteristics, and more particularly to a method and system for determining the elastic modulus of a material along the longitudinal axis thereof.
(2) Description of the Prior Art
To predict the dynamic response of a structure, it is necessary to measure the stiffness and loss properties of materials one important property is the elastic modulus which is a complex value having a real part corresponding to energy transmission and an imaginary part corresponding to energy attenuation. Resonant techniques for measuring stiffness and loss have been used by researchers for many years and are based on measuring the eigenvalues of a structure and comparing them to eigenvalues of a model of the same structure. The structure must have well-defined eigenvalues and eigenvectors for the method to be successful. However, structural materials that are placed under tension (with masses or ropes) do not have closed-form eigenvectors, and their eigenvalues must be calculated with a transcendental equation. Additionally, this test only allows measurements at resonances.
Some material testing machines are designed to excite pieces of materials in a manner that allows investigation of stiffness and loss. However, the typically small test samples cannot be subjected to significant tensile forces because of their size. Another approach for measuring stiffness and loss parameters compares analytical models to measured frequency response functions. However, most of these methods tend to be computationally intensive, and the fitting routines do not always converge to the correct answer, especially when more than one unknown parameter of the model must be estimated.
More recently, methods have been developed to determine the elastic modulus of a material. Some methods use strain gauges which can be physically intrusive when measuring the properties of soft materials. Another method of measuring the elastic modulus is presented in U.S. Pat. No. 4,418,573. The method of the '573 patent utilizes system phase angle relations to determine where, in frequency, a measurement can be made. However, this approach does not provide measurements at all frequencies since measurements are only possible at the occurrence of zero phase angles--a situation that does not occur at all frequencies.